Recent international climate negotiations suggest that complete agreements are unlikely to materialize. Instead, partial cooperation between like-minded countries appears a more likely outcome. In this paper we analyze the effects of such partial cooperation between like-minded countries. In doing so, we link the literature on partial cooperation with so-called matching approaches. Matching schemes are regarded as providing a promising approach to overcome undersupply of public goods like climate protection. The functioning of matching mechanisms in a setting with an incomplete agreement, i.e. a contract where only a subset of the players participates, has however not been investigated yet. This paper fills this research gap by analyzing incomplete matching agreements in the context of international climate protection. We analyse their effect on both welfare and the global climate protection level. We show that matching coalitions may bring about a decline in global public good provision and a reduction in the welfare of outsiders.